What powered the Time Machine?

The basic premise was the crystal on the handle. This is inferred in the featurette, Time Machine: The Journey Back. There's a kind of pseudo mysticism surrounding crystals, as you probably know.

There was also a plausibility suggestion intended for the big disc behind the seat. It had 365 markings around the circumference, indicating time measurement in years. And the featurette stated that it was planned that the disc would rotate in opposite directions for forward and backward in time, but that was not possible with the budget, as I recall.

So the crystal was apparently the power, and the big disc was the regulator.
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The story is king.

It's all about electricity, magnetism, electromagnetism and electric fields. It was the big thing in those years. In 1895 Wilhelm Conrad Röntgen discovered the X-Rays, for the people of the late 19th century a magic electric lamp produces magic see-through pictures. This sensation nuked the scientific world of 1895. Maybe Wells was influenced by this too.

The spinning disc could contain cables, conductors, projectors, transmisstion lines, antennas, which then would generate the four-dimensional time travelling field. All powered by miniaturiued batteries.

Higher dimensonal scifi-devices are often related with spinning things, producing spinning fields. The FTL drive of the "Battlestar Galactica" had large spinning machines as jump drive. The "Serenity" ship from Firefly has a spinning back. Same thing with Ronan's "Dark Aster" ship from Guardians of the Galaxy. In a fight scene with Korath we can see several big spinning machines, eventually producing vortex fields for travelling and artificial gravity. The wormhole device from "Contact" with Jodie Foster worked with large spinning contraptions. Another example is the Bifrost travelling device in the Thor movies, when the heroes start at the ramp in Heimdall's dome. In the Time Machine remake from 2002 there were also lots of spinning fields and lights.

The Flux Capacitor of course !